The multifractal formalism is a heuristic relationship introduced in [1]} which relates the \(L^q\) -spectrum and the multifractal spectrum of \(\mu \)  under certain conditions.

Given \(\alpha \in \) , we say that the measure \(\mu \)  satisfies the multifractal formalism at \(\alpha \)  if
\(f_\mu (\alpha )=\tau _\mu ^*(\alpha )\) 
